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Question
The mass of balloon and its contents is M. It is descending with an acceleration a. By how much the mass should be decreased, keeping the volume constant, so that the balloon starts ascending with the same acceleration?
The mass of balloon and its contents is M. It is descending with an acceleration a. By how much the mass should be decreased, keeping the volume constant, so that the balloon starts ascending with the same acceleration?
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Solution
The correct option is C 2aa+gM
The forces acting on the balloon when the balloon is coming downwards with an acceleration a are
(i) weight, mg acting downwards and
(ii) the force of upthrust, F acting upwards. Since the accelerated movement is in the downward direction, the force Mg must be greater than F. So for the downwards accelerated movement of the block,
Mg−F=Ma..........(i)
Let m be the mass removed from the balloon, the weight of the balloon now becomes (M−m)g. Now for the upward accelerated movement with the same acceleration, we have
F−(M−m)g=(M−m)a.......(ii)
Solving equations, (i) and (ii) (Mg−Mg)−Mg+mg=Ma−maor m(g+a)=2Mam=2Mag+a.
The forces acting on the balloon when the balloon is coming downwards with an acceleration a are
(i) weight, mg acting downwards and
(ii) the force of upthrust, F acting upwards. Since the accelerated movement is in the downward direction, the force Mg must be greater than F. So for the downwards accelerated movement of the block,
Mg−F=Ma..........(i)
Let m be the mass removed from the balloon, the weight of the balloon now becomes (M−m)g. Now for the upward accelerated movement with the same acceleration, we have
F−(M−m)g=(M−m)a.......(ii)
Solving equations, (i) and (ii)
(Mg−Mg)−Mg+mg=Ma−ma
or m(g+a)=2Ma
m=2Mag+a.
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